Slope Of Line 5A98D7

1. **State the problem:** We are given the linear equation $$1.5x + 4.5y = 18$$ and asked to find the slope of its graph. 2. **Rewrite the equation in slope-intercept form:** The slope-intercept form is $$y = mx + b$$ where $$m$$ is the slope. 3. **Isolate $$y$$:** $$1.5x + 4.5y = 18$$ Subtract $$1.5x$$ from both sides: $$4.5y = 18 - 1.5x$$ 4. **Divide both sides by $$4.5$$ to solve for $$y$$:** $$y = \frac{18 - 1.5x}{4.5}$$ Use the property of fractions: $$y = \frac{18}{4.5} - \frac{1.5x}{4.5}$$ Simplify each term: $$\frac{18}{4.5} = 4$$ and $$\frac{1.5}{4.5} = \frac{\cancel{1.5}}{\cancel{4.5}} = \frac{1}{3}$$ So, $$y = 4 - \frac{1}{3}x$$ 5. **Rewrite in slope-intercept form:** $$y = -\frac{1}{3}x + 4$$ 6. **Identify the slope:** The slope $$m$$ is the coefficient of $$x$$, which is $$-\frac{1}{3}$$. **Final answer:** The slope of the graph is $$-\frac{1}{3}$$.